Direct and inverse scattering problems for nonlinear dispersive equations with potential

• Project/Area Number: 22740082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Chiba University
• Principal Investigator: SASAKI Hironobu 千葉大学, 大学院・理学研究科, 准教授 (00568496)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 非線型分散型方程式 / ディラック方程式 / 漸近挙動 / 散乱作用素 / 波動作用素 / ソボレフ空間 / 時間減衰評価 / 線型作用素 / 非線型ディラック方程式 / ストリッカーツ評価 / 重み付ソボレフ空間 / 解の漸近挙動 / 短距離散乱 / 減衰評価 / 非線型シュレディンガー方程式 / 散乱問題 / 逆散乱問題 / 相互作用ポテンシャル

Research Abstract

In this study, we consider direct and inverse scattering problems for dispersive equations. By using methods of functional analysis, we obtain results for inverse scattering problems for Hartree equations in three space dimensions, direct and inverse scattering problems for the Klein-Gordon equation in quantum field theory and scattering problems for nonlinear Dirac equations in one space dimension.

Research Products

• [Journal Article] Scattering problems for the one-dimensional nonlinear Dirac equation with power nonlinearity (2013)
  • Author(s): H.Sasaki
  • Journal Title: Journal of Physics: Conference Series Volume: 410 Pages: 12035-12035
  • URL: http://iopscience.iop.org/1742-6596/410/1/012035
  • Peer Reviewed
• [Journal Article] Scattering problems for the one-dimensional nonlinear Dirac equation with power nonlinearity (2013)
  • Author(s): Hironobu Sasaki
  • Journal Title: Journal of Physics: Conference Series Volume: 410 Pages: 12035-12035
  • Peer Reviewed
• [Journal Article] Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly (2012)
  • Author(s): H.Sasaki
  • Journal Title: J. Differential Equations Volume: 252 Pages: 2004-2023
  • Peer Reviewed
• [Journal Article] Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly (2012)
  • Author(s): H.Sasaki
  • Journal Title: J.Differential Equations Volume: 252 Pages: 2004-2023
  • Peer Reviewed
• [Journal Article] An inverse scattering problem for the Klein-Gordon equation with a classical source in quantum field theory (2011)
  • Author(s): H.Sasaki and A.Suzuki
  • Journal Title: Hokkaido Math.J. Volume: 40 Pages: 149-186
  • Peer Reviewed
• [Presentation] Scattering problems for the one-dimensional nonlinear Dirac equation with power nonlinearity (2012)
  • Author(s): 佐々木 浩宣
  • Organizer: 日本数学会 2012 年度秋季総合分科会函数方 程式論分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-20
• [Presentation] Scattering problems for the one-dimensional nonlinear Dirac equation with power nonlinearity (2012)
  • Author(s): 佐々木 浩宣
  • Organizer: 日本数学会2012年度秋季総合分科会函数方程式論分科会
  • Place of Presentation: 九州大学
• [Presentation] 急減少する相互作用ポテンシャルを持つHartree型方程式の逆散乱問題 (2011)
  • Author(s): 佐々木浩宣
  • Organizer: 日本数学会2011年度年会函数方程式論分科会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-22
• [Presentation] 急減少する相互作用ポテンシャルを持つHartree型方程式の逆散乱問題 (2011)
  • Author(s): 佐々木浩宣
  • Organizer: 日本数学会
  • Place of Presentation: 早稲田大学(東京都)
  • Year and Date: 2011-03-22
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~sasaki/J-re.html
• [Remarks] webページ
  • URL: http://www.math.s.chiba-u.ac.jp/~sasaki/
• [Remarks] 研究内容又は研究成果に関するwebページ:
  • URL: http://www.math.s.chiba-u.ac.jp/~sasaki/
• [Remarks] 上記日本数学会は震災の影響で中止となったが、アブストラクト集の発行をもって、講演が成立したものと見做されることになった。
  • URL: http://mathsoc.jp/meeting/wasedallmar/record2011.html